Classification of infinitely differentiable periodic functions

• Date: 2008
• Main Authors: Serdyuk, A. S., Stepanets, O. I., Shydlich, A. L., Сердюк, А. С., Степанец, А. И., Шидлич, А. Л.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2008
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3282
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

The set $\mathcal{D}^{\infty}$ of infinitely differentiable periodic functions is studied in terms of generalized $\overline{\psi}$-derivatives defined by a pair $\overline{\psi} = (\psi_1, \psi_2)$ of sequences $\psi_1$ and $\psi_2$. In particular, it is established that every function $f$ from t...